Explanation Given: y = 1 3 x 3 2 − x 1 2 , [ 2 , 8 ] Key Concept and Formula Used: The arc length s of function y = f ( x ) over [ a , b ] is equal to s = ∫ a b 1 + ( f ' ( x ) ) 2 d x d d x x n = n x n − 1 and ∫ x n d x = x n + 1 n + 1 + C Calculation: To calculate the arc length we first differentiate the given function and then use the formula to find the arc length. y = 1 3 x 3 2 − x 1 2 = f ( x ) f ' ( x ) = d d x [ 1 3 x 3 2 − x 1 2 ] = 3 2 × 1 3 ( x ) 3 2 − 1 − 1 2 x 1 2 − 1 = 1 2 x 1 2 − 1 2 x − 1 2 f ' ( x ) = 1 2 [ x − 1 x ] Arc length= s = ∫ a b 1 + ( f ' ( x ) ) 2 d x where a = 2 & b = 8 s = ∫ 2 8 1 +

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 8E

To determine

the arc length over the given interval.

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Chapter 9.2, Problem 7E

Chapter 9.2, Problem 9E

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Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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